1. Technical Field
The present invention relates to scaling binary images. More particularly, the present invention relates to binary image scaling by piecewise polynomial interpolation.
2. Description of the Prior Art
When scaling a binary image, it is necessary to resolve the discrepancy between the input resolution and the output resolution. For example, in facsimile imaging the original images are transmitted at a standard resolution, typically 203 dots per inch ("dpi") in the row direction and 98 dpi in the column direction, and printed at the printer resolution, e.g. 300 dpi, in both the row and column directions. Another example of binary imaging involves font scaling, for example when a 12 point font at 300 dpi is to be used as a 24 point font and printed on a 600 dpi printer, the original image must be scaled by a factor of four. Thus, the scaling factor can be an integer or a fractional number.
One approach to image scaling is to apply piecewise polynomial interpolation such as B-splines, as proposed in R. V. Klassen, R. H. Bartels, Using B-splines for Re-Sizing Images, University of Waterloo, Department of Computer Science, Technical Report, 1986. However, such approach has not proven satisfactory.
A quantization error problem embedded in all piecewise polynomial interpolants for scaling was reported in I. E. Abdou and K. Y. Wong, Analysis of Linear Interpolation Schemes for Bi-Level Image Applications, IBM J. Res. Develop., V. 26, No. 6, pp. 667-680, November, 1982. Thus, interpolation schemes give rise to a quantization error problem, such that the image stroke width is not preserved after image scaling.
Other known approaches for scaling and smoothing images include pixel-replication, contour-tracing (see W. Rutkowski, Shape Completion, Computer Graphics and Image Processing, Vol. 9, pp. 89-101, 1979), cubic B-spline interpolation (see H. S. Hou, H. C. Andrews, Cubic Splines for Image Interpolation and Digital Filtering, IEEE Transaction on Acoustic, Speech and Signal Processing, Vol. ASSP-26, pp. 508-517), template based scaling (see R. A. Ulichney, D. E. Troxel, Scaling Binary Images with the Telescoping Template, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-4, No. 3, pp. 331-335, 1982), and extrapolative prediction (see C. Tung, Resolution Enhancement Technology in Hewlett Packard Laser Jet Printers, IST/SPIE Symposium on Electronic Imaging: Science and Technology, pp. 440-448, 1993).
There is not known a satisfactory and flexible scheme based on automatic numerical computation for binary image scaling that is general enough for all integer and fractional scaling factors, while avoiding quantization problems typically encountered in prior art approaches using piecewise polynomial interpolants.